JSET ejournal
Effects of Video-Based and
Applied Problems on the Procedural Math Skills of Average- and
Low-Achieving Adolescents
Brian A. Bottge
University of WisconsinMadison
Mary Heinrichs
Wisconsin Center for Education Research
Shih-Yi Chan
National Tainan Teachers College, Taiwan
Zara Dee Mehta
Elizabeth Watson
University of WisconsinMadison
The National Council of Teachers of Mathematics (NCTM) recommends
that all students have opportunities to solve meaningful and
complex math problems (National Council of Teachers of Mathematics,
2000). According to NCTM, the quality of such opportunities should
be judged by their effect on the student-that is, opportunities
are valuable when they help "students become confident in
their ability to tackle difficult problems, eager to figure things
out on their own, flexible in exploring mathematical ideas and
trying alternative paths, and willing to persevere" (NCTM,
2000, p. 21). Recent test results show that the emphasis on mathematics
may be paying off. In the latest National Assessment of Educational
Progress (NAEP) (U.S. Department of Education, 2001), fourth-grade,
eighth-grade, and 12th-grade students scored higher in the year
2000 than in 1990.
Although the NAEP results showed higher math achievement for
most students overall, they also revealed that more than one
third (34%) of eighth-grade students scored below basic levels,
which include understanding arithmetic operations with whole
numbers and fractions. The performance of students with disabilities
on the NAEP tests was not analyzed separately, but it is likely
that disproportionate numbers of these students were at the basic
level because research has consistently documented their low
achievement in basic arithmetic (Cawley, Parmar, Foley, Salmon,
& Roy, 2001; Cawley, Parmar, Yan, & Miller, 1998; Kavale
& Reese, 1992) and problem solving (Jitendra, Hoff, &
Beck, 1999; Montague & Applegate, 1993; Parmar, Cawley, &
Frazita, 1996; Xin & Jitendra, 1999). Moreover, studies show
that students with disabilities do not catch up to their average-achieving
(AA) classmates (Cawley, Kahn, & Tedesco, 1989) and eventually
drop out of school (Phelps & Hanley-Maxwell, 1997).
Computing rational numbers represented as fractions is more difficult
than computing whole numbers for most students and especially
for low-achieving (LA) students (Behr, Lesh, Post, & Silver,
1983; Behr, Wachsmuth, & Post, 1985; Kerslake, 1986). Even
high-achieving middle school and high school students do not
always compute fractions in a straightforward manner. For example,
Smith (1995) reported that capable students used more than 20
different strategies to help them compare the relative size of
fractions and compute missing addends. The most common of these
procedures involved computation-intensive strategies to alter
the representation of fractions to equivalent fractions with
common denominators.
In their efforts to remediate skill deficits in math, teachers
of LA students often overemphasize fact retrieval, rote mastery
of algorithms, and key word strategies (Anyon, 1981; Haberman,
1991; Hiebert et al., 1996; Woodward & Baxter; 1997), practices
that limit opportunities for LA students to work on problems
that interest them (Gersten, 1998; Gersten & Chard, 1999;
Knapp & Turnbull, 1990; Woodward & Howard, 1994; Woodward,
Baxter, & Robinson, 1999). This adds to LA students' dislike
of mathematics, reduces their motivation, and leads to bizarre
solutions to real problems (Thorndike, 1922; Whitehead, 1929).
In addition, many students with difficulties in math also have
low reading skills, which makes it difficult for them to visualize
the problems embedded in text (Norman, 1983; Shepard & Cooper,
1982).
For almost a decade, researchers have studied ways to improve
LA students' math skills using a pedagogical approach called
anchored instruction. Anchored instruction is a way of
situating, or anchoring, the learning of students in problems
that seem authentic and meaningful to them, thus motivating them
to use and enhance their understandings of math. Researchers
have sought to engage the interest of LA students by having them
solve video-based problems delivered on CD-ROM (called anchors)
(Bottge, 1999; Bottge, Heinrichs, Mehta, & Hung, 2002; Bransford,
et al., 1988; Bransford, et al., 1996; Hickey, Moore, & Pellegrino,
2001). A series of problem-solving anchors called the New
Adventures of Jasper Woodbury (Learning Technology Center
at Vanderbilt University, 1996) situate interesting problems
in a video format, enabling students to immediately access the
problems without having to decode and comprehend word-based problems.
Three video-based anchors containing less complex problems have
also been developed specifically for LA students (Bottge &
Hasselbring, 1993). These motivating problems do not explicitly
state or direct students toward one specific solution as most
standard word problems do. Instead, students are responsible
for searching the contents of the video for relevant information
that can be used to solve the problem. The effectiveness of anchored
instruction depends on a rich, realistic source of information
and guidance by an effective teacher.
